If x represents an even integer, which expression
also represents an even integer?
1. 2x+1
2. 2x
3. x+1
4. x-1

Arbitrarily select an even number for x and substitute.

I will arbitrarily select the even number 8. I could choose 6 or 10
or 74 or  2 or 50 or 2000000.  But I'll stick with 8.

So let x = 8

Substitute 8 for x in the choices till you find it:

1. 2x+1
2. 2x
3. x+1
4. x-1

becomes

1. 2x+1 = 2(8)+1 = 16+1 = 17, nope that's an odd number
2. 2x   = 2(8) = 16, yep that's an even number 
(so that's the correct choice, but let's check the other
ones anyway, to show that they are not even)
3. x+1 = (8)+1 = 9, nope that's an odd number
4. x-1 = (8)-1 = 7, nope that's an odd number.

Edwin